Question

A staff is placed on a benchmark (BM) of reduced level (RL) $100.000\text{m}$ and a theodolite is placed at a horizontal distance of $50\text{m}$ from the BM to measure the vertical angles. The measured vertical angles from the horizontal at the staff readings of $0.400\text{m}$ and $2.400\text{m}$ are found to be the same. Taking the height of the instrument as $1.400\text{m}$, the RL (in $\text{m}$) of the theodolite station is

• A. 100

Answer 1

The correct option is A 100

$\tan \theta =\frac{2.4-x}{50}=\frac{x-0.4}{50}$

$2x=2.8$

$x=1.4\text{m}$

H.O.I. $=100+1.4$

$=101.4\text{m}$

$\text{RL of theodolite station = 101.4 - Theodolite height}$

$=101.4-1.4$

$=100\text{m}$